Fourier Coefficients of Vector-valued Modular Forms of Dimension $2$

Canadian mathematical bulletin

Geoffrey Mason¹  Cameron Franc¹ 

[1] Department of Mathematics, University of California, Santa Cruz

关键词: vector-valued modular form;    modular group;    bounded denominators;   

DOI  :  10.4153/CMB-2014-007-3

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We prove the following Theorem. Suppose that $F=(f_1, f_2)$ is a $2$-dimensional vector-valued modular formon $operatorname{SL}_2(mathbb{Z})$ whose component functions $f_1, f_2$ have rational Fourier coefficientswith bounded denominators. Then $f_1$ and $f_2$ are classical modular forms on a congruence subgroup of the modular group.

【 授权许可】

Unknown